Abstract

We show theoretical evidence that coherent systems based on electromagnetically induced transparency (EIT) can function as optically addressed spatial light modulators with megahertz modulation rates. The transverse spatial properties of cw probe fields can be modulated fast using two-dimensional optical patterns. To exemplify our proposal, we study real-time generation and manipulation of Laguerre–Gaussian beams by means of phase or amplitude modulation using flat-top image-bearing pulse trains as coupling fields in low-cost hot vapor EIT systems.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. U. Efron, ed., Spatial Light Modulator Technology. (Marcel Dekker, 1994).
  2. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
    [CrossRef] [PubMed]
  3. S. Barreiro and J. W. R. Tabosa, Phys. Rev. Lett. 90, 133001 (2003).
    [CrossRef] [PubMed]
  4. P. Z. Dashti, F. Alhassen, and H. P. Lee, Phys. Rev. Lett. 96, 043604 (2006).
    [CrossRef] [PubMed]
  5. D. Akamatsu and M. Kozuma, Phys. Rev. A 67, 023803 (2003).
    [CrossRef]
  6. L. Chen and W. She, Opt. Lett. 33, 696 (2008).
    [CrossRef] [PubMed]
  7. L. Chen and W. She, Opt. Lett. 34, 178 (2009).
    [CrossRef] [PubMed]
  8. G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
    [CrossRef]
  9. D. G. Grier, Nature 424, 810 (2003).
    [CrossRef] [PubMed]
  10. F. K. Fatemi and M. Bashkansky, Opt. Express 14, 1368 (2006).
    [CrossRef] [PubMed]
  11. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
    [CrossRef] [PubMed]
  12. J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, Nat. Phys. 4, 282 (2008).
    [CrossRef]
  13. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
    [CrossRef]
  14. M. D. Lukin, Rev. Mod. Phys. 75, 457 (2003).
    [CrossRef]
  15. H. Schmidt and R. J. Ram, Appl. Phys. Lett. 76, 3173 (2000).
    [CrossRef]
  16. S. E. Harris and L. F. Luo, Phys. Rev. A 52, R928 (1995).
    [CrossRef] [PubMed]
  17. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
    [CrossRef]
  18. D. A. Steck, Rubidium 87 D Line Data, available online at http://steck.us/alkalidata (revision 2.1, September 1, 2008).
  19. J. E. Curtis and D. G. Grier, Opt. Lett. 28, 872 (2003).
    [CrossRef] [PubMed]
  20. M. Fleischhauer and A. S. Manka, Phys. Rev. A 54, 794 (1996).
    [CrossRef] [PubMed]
  21. N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
    [CrossRef]
  22. G. F. Brand, J. Mod. Opt. 44, 1243 (1997).
    [CrossRef]
  23. G. F. Brand, Am. J. Phys. 67, 55 (1999).
    [CrossRef]

2009 (1)

2008 (2)

J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, Nat. Phys. 4, 282 (2008).
[CrossRef]

L. Chen and W. She, Opt. Lett. 33, 696 (2008).
[CrossRef] [PubMed]

2007 (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

2006 (2)

F. K. Fatemi and M. Bashkansky, Opt. Express 14, 1368 (2006).
[CrossRef] [PubMed]

P. Z. Dashti, F. Alhassen, and H. P. Lee, Phys. Rev. Lett. 96, 043604 (2006).
[CrossRef] [PubMed]

2005 (1)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

2003 (5)

M. D. Lukin, Rev. Mod. Phys. 75, 457 (2003).
[CrossRef]

D. Akamatsu and M. Kozuma, Phys. Rev. A 67, 023803 (2003).
[CrossRef]

D. G. Grier, Nature 424, 810 (2003).
[CrossRef] [PubMed]

J. E. Curtis and D. G. Grier, Opt. Lett. 28, 872 (2003).
[CrossRef] [PubMed]

S. Barreiro and J. W. R. Tabosa, Phys. Rev. Lett. 90, 133001 (2003).
[CrossRef] [PubMed]

2001 (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

2000 (1)

H. Schmidt and R. J. Ram, Appl. Phys. Lett. 76, 3173 (2000).
[CrossRef]

1999 (1)

G. F. Brand, Am. J. Phys. 67, 55 (1999).
[CrossRef]

1997 (1)

G. F. Brand, J. Mod. Opt. 44, 1243 (1997).
[CrossRef]

1996 (1)

M. Fleischhauer and A. S. Manka, Phys. Rev. A 54, 794 (1996).
[CrossRef] [PubMed]

1995 (1)

S. E. Harris and L. F. Luo, Phys. Rev. A 52, R928 (1995).
[CrossRef] [PubMed]

1994 (1)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

1992 (2)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

Akamatsu, D.

D. Akamatsu and M. Kozuma, Phys. Rev. A 67, 023803 (2003).
[CrossRef]

Alhassen, F.

P. Z. Dashti, F. Alhassen, and H. P. Lee, Phys. Rev. Lett. 96, 043604 (2006).
[CrossRef] [PubMed]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Barreiro, J. T.

J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, Nat. Phys. 4, 282 (2008).
[CrossRef]

Barreiro, S.

S. Barreiro and J. W. R. Tabosa, Phys. Rev. Lett. 90, 133001 (2003).
[CrossRef] [PubMed]

Bashkansky, M.

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Brand, G. F.

G. F. Brand, Am. J. Phys. 67, 55 (1999).
[CrossRef]

G. F. Brand, J. Mod. Opt. 44, 1243 (1997).
[CrossRef]

Chen, L.

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Curtis, J. E.

Dashti, P. Z.

P. Z. Dashti, F. Alhassen, and H. P. Lee, Phys. Rev. Lett. 96, 043604 (2006).
[CrossRef] [PubMed]

Efron, U.

U. Efron, ed., Spatial Light Modulator Technology. (Marcel Dekker, 1994).

Fatemi, F. K.

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

M. Fleischhauer and A. S. Manka, Phys. Rev. A 54, 794 (1996).
[CrossRef] [PubMed]

Grier, D. G.

Harris, S. E.

S. E. Harris and L. F. Luo, Phys. Rev. A 52, R928 (1995).
[CrossRef] [PubMed]

Heckenberg, N. R.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Kozuma, M.

D. Akamatsu and M. Kozuma, Phys. Rev. A 67, 023803 (2003).
[CrossRef]

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Kwiat, P. G.

J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, Nat. Phys. 4, 282 (2008).
[CrossRef]

Lee, H. P.

P. Z. Dashti, F. Alhassen, and H. P. Lee, Phys. Rev. Lett. 96, 043604 (2006).
[CrossRef] [PubMed]

Lukin, M. D.

M. D. Lukin, Rev. Mod. Phys. 75, 457 (2003).
[CrossRef]

Luo, L. F.

S. E. Harris and L. F. Luo, Phys. Rev. A 52, R928 (1995).
[CrossRef] [PubMed]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Manka, A. S.

M. Fleischhauer and A. S. Manka, Phys. Rev. A 54, 794 (1996).
[CrossRef] [PubMed]

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

McDuff, R.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Ram, R. J.

H. Schmidt and R. J. Ram, Appl. Phys. Lett. 76, 3173 (2000).
[CrossRef]

Rubinsztein-Dunlop, H.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

Schmidt, H.

H. Schmidt and R. J. Ram, Appl. Phys. Lett. 76, 3173 (2000).
[CrossRef]

She, W.

Smith, C. P.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Steck, D. A.

D. A. Steck, Rubidium 87 D Line Data, available online at http://steck.us/alkalidata (revision 2.1, September 1, 2008).

Tabosa, J. W. R.

S. Barreiro and J. W. R. Tabosa, Phys. Rev. Lett. 90, 133001 (2003).
[CrossRef] [PubMed]

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Wegener, M. J.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

Wei, T.-C.

J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, Nat. Phys. 4, 282 (2008).
[CrossRef]

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Am. J. Phys. (1)

G. F. Brand, Am. J. Phys. 67, 55 (1999).
[CrossRef]

Appl. Phys. Lett. (1)

H. Schmidt and R. J. Ram, Appl. Phys. Lett. 76, 3173 (2000).
[CrossRef]

J. Mod. Opt. (1)

G. F. Brand, J. Mod. Opt. 44, 1243 (1997).
[CrossRef]

Nat. Phys. (2)

J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, Nat. Phys. 4, 282 (2008).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Nature (2)

D. G. Grier, Nature 424, 810 (2003).
[CrossRef] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Opt. Commun. (1)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Opt. Quantum Electron. (1)

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

Phys. Rev. A (4)

D. Akamatsu and M. Kozuma, Phys. Rev. A 67, 023803 (2003).
[CrossRef]

M. Fleischhauer and A. S. Manka, Phys. Rev. A 54, 794 (1996).
[CrossRef] [PubMed]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

S. E. Harris and L. F. Luo, Phys. Rev. A 52, R928 (1995).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

S. Barreiro and J. W. R. Tabosa, Phys. Rev. Lett. 90, 133001 (2003).
[CrossRef] [PubMed]

P. Z. Dashti, F. Alhassen, and H. P. Lee, Phys. Rev. Lett. 96, 043604 (2006).
[CrossRef] [PubMed]

Rev. Mod. Phys. (2)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

M. D. Lukin, Rev. Mod. Phys. 75, 457 (2003).
[CrossRef]

Other (2)

D. A. Steck, Rubidium 87 D Line Data, available online at http://steck.us/alkalidata (revision 2.1, September 1, 2008).

U. Efron, ed., Spatial Light Modulator Technology. (Marcel Dekker, 1994).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

(a) Three-level Λ atomic system and two copropagating light fields with a small detuning Δ. (b) Uniform illumination of the coupling field imposing no phase shift onto the incident Gaussian probe field ( l = 0 ) . (c) Azimuthal intensity of the coupling field to generate the LG beam with l = 1 , where ϕ is the azimuthal angle. The intensity could be shown numerically in Fig. 2a. (d) l = 2 . (e) Possible experimental setup. Two image-bearing flat-top pulse trains, which are complementary in the time domain, are adopted to fast switch the images. For the pulse train 0 (1), which bears the image for l = 0 ( l = 1 ) , the repetition period is T 0 ( T 1 ) and the pulse duration is t 0 ( t 1 ) . We here assume t 0 = t 1 = T 0 2 = T 1 2 = T 2 and one train is delayed by half a cycle with respect to the other one. BS, beam splitter. PBS, polarizing beam splitter.

Fig. 2
Fig. 2

(a) Azimuthal intensity I ( ϕ ) ( = ϵ 0 c E c ( ϕ ) 2 2 ) of the coupling field (solid curve) cor responding to Fig. 1c with a = 500 , b = c = 1 for Ω c ( ϕ ) ( = a ( b ϕ + c ) γ 31 ) , where I ( 0 ) = 838 mW cm 2 and I ( 2 π ) = 115 mW cm 2 . In experiments, these intensities can be easily obtained [13]. According to Eq. (2), this azimuthal intensity of the strong coupling field can induce a linearly ϕ-dependent refractive index and low absorption for the probe field. Thus also shown is the high transmission rate T ( ϕ ) > 90 % of the cw probe field (dashed curve). (b) Linear susceptibility for the probe field in Rb 87 induced by the azimuthal intensity of the coupling field in (a). The real part χ (solid curve) is associated with the linearly ϕ-dependent refractive index and the imaginary part χ (dashed curve) is associated with the low absorption.

Fig. 3
Fig. 3

(a) Forked binary amplitude grating to generate the LG modes with l = ± 1 . (b) l = ± 2 .

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

χ = χ + i χ = μ 13 2 ϱ × 4 Δ Ω c 2 + i 8 Δ 2 γ 31 + i 2 γ 21 d ( Ω c 2 + γ 31 γ 21 d ) ϵ 0 Ω c 2 + γ 31 ( γ 21 d i 2 Δ ) 2 .
χ Δ Ω c 2 , χ 4 Δ 2 γ 31 + γ 21 d Ω c 2 Ω c 4 0 ,
d [ Δ n ( ϕ ) ] = d [ χ ( 2 π ) χ ( 0 ) ] 2 = Δ l λ ,
χ = 2 μ 13 2 ϱ ϵ 0 γ 31 0.0072 , T = e α d e 29 0 ,
t f ( r , ϕ ) = 1 2 + k = 0 2 sin [ ( 2 k + 1 ) ( l ϕ + 2 π D r cos ϕ ) ] ( 2 k + 1 ) π ,

Metrics